Light is quite difficult to propagate a long distance in random media such as human tissue or atmospheric dense cloud because of its scattering and absorption. For optical sensing, it is important to increase propagation efficiency which means expanding the sensing range. An annular beam can transform its waveform into a non-diffractive beam due to its propagation in a long distance. In our previous work, we found the annular beam also had non-diffractive effect when it propagated in diluted milk solution of a few tens centimetres at the concentration of less than 1%. In this study, to clear up how to control and optimize the non-diffractive effect of the annular beam in random media, numerical calculation of propagation characteristics of annular beam in air was estimated. The narrow annular beam with a small diameter would generate a high intensity non-diffractive beam at a short distance. We also had three sets of experiments of annular beam propagation in random media with the same view point as the calculation, but its propagation characteristics was evaluated by milk concentration. They showed the same variation of a non-diffractive beam with the result of numerical calculation in air. These results provide us a hint of optimization for annular beam propagation in random media.